<span>40 units2˛ Looking at the figure, the rectangle has the vertexes (2,1), (3,-3), (-5,-5) and (-6,-1). The parallelogram has the vertexes (2,7), (3,3), (3,-3), and (2,1).
The area of a parallelogram is base times height. We have 2 vertical lines at x=2 and x=3, so the height is 1. And the length of the line from (3,3) to (3,-3) is 6, so the base is 6. Therefore the area of the parallelogram is 1*6 = 6.
The rectangle is a tad trickier since it's not aligned with either the x or y axis. But we can use the Pythagorean theorem to get the lengths.
L = sqrt((2 - -6)^2 + (1 - -1)^2)
L = sqrt(8^2 + 2^2)
L = sqrt(64 + 4) L = sqrt(68) = 2*sqrt(17)
W = sqrt((2-3)^2 + (1- -3)^2)
W = sqrt((-1)^2 + 4^2)
W = sqrt(1 + 16)
W = sqrt(17)
And the area is length * width, so:
2*sqrt(17)*sqrt(17) = 2 * 17 = 34
And the total area is the sum of the areas, so
34 + 6 = 40
So the area of the figure is 40 square units.</span>
Given the coordinates of two points, P1 and P2, the distance formula between these two points is deduced. d = root ((x2-x1) ^ 2 + (y2-y1) ^ 2) To find the area of the figure we must first find the area of the rectangle and add the area of the parallelogram. rectangle area A = (L) * (w) L = root ((- 6-2) ^ 2 + (- 1-1) ^ 2) = 8.25 w = root ((- 6 - (- 5)) ^ 2 + (- 1 - (- 5)) ^ 2) = 4.12 A = (8.25) * (4.12) = 33.99 Parallelogram area A = (b) * (h) b = root ((3-3) ^ 2 + (3 - (- 3)) ^ 2) = 6 h = root ((3-2) ^ 2 + (3-3) ^ 2) = 1 A = (6) * (1) = 6 The total area is then Atotal = 33.99 + 6 = 39.99 units ^ 2 Answer the area of this figure is 39.99 units ^ 2
